[SOLVED] Integral estimation

• Mar 30th 2008, 04:51 PM
topsquark
[SOLVED] Integral estimation
Quote:

Using 20 terms, estimate f(0.6) where
$f(x) = \int_0^x \frac{dt}{1 + t^3}$
The student was trying to do this using a geometric series to represent the integrand. I haven't yet looked it up in my Calc book, but if I ever knew the method I've completely forgotten it. Any takers?

Thanks!
-Dan
• Mar 30th 2008, 04:55 PM
Krizalid
$f(x) = \int_0^x {\left\{ {\sum\limits_{k\, = \,0}^\infty {( - 1)^k t^{3k} } } \right\}\,dt} .$

After interchanging sum & integral you'll get its series representation.
• Mar 30th 2008, 05:24 PM
topsquark
Quote:

Originally Posted by Krizalid
$f(x) = \int_0^x {\left\{ {\sum\limits_{k\, = \,0}^\infty {( - 1)^k t^{3k} } } \right\}\,dt} .$

After interchanging sum & integral you'll get its series representation.

-Dan
• Mar 30th 2008, 06:19 PM
ThePerfectHacker
How about proving the accurarcy after using 20 terms? That sounds like a more interesting problem.
• Mar 30th 2008, 07:08 PM
topsquark
Quote:

Originally Posted by ThePerfectHacker
How about proving the accurarcy after using 20 terms? That sounds like a more interesting problem.

(snorts) These are Calc I High School students. Maybe AP maybe not. I'm not going to go into that kind of thing with them unless they force me to with hot irons, kicking and screaming "You can't have your pudding if you don't eat your meat!"

-Dan